Download "Найдите все такие простые числа p и q , что p + q = (p – q)³"

"videoThumbnail Найдите все такие простые числа p и q , что p + q = (p – q)³

Ананас из бумаги. Объёмная поделка. Красиво и просто!

Ананас из бумаги. Объёмная поделка. Красиво и просто!

Channel: Ксения Филиппова

Почему математики не тратят время на лотереи

Почему математики не тратят время на лотереи

Channel: QWERTY

Вторая луна Земли? Поразительные орбиты планет Солнечной системы [Numberphile на русском]

Вторая луна Земли? Поразительные орбиты планет Солнечной системы [Numberphile на русском]

Channel: Solipschism

математика

изучаем математику

вступительные по математике

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let's look at the solution to a problem like this,

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find all such prime numbers P

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and Q that such an equality holds, the

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key word here is simple means by

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IQ These are prime numbers, let's remember prime

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numbers are natural numbers that

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have exactly 2 divisors the number itself and

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one, or otherwise a

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prime number this is a number that is different from

00:00:27

one and can be divided without a remainder by the

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number itself and one

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by

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everything else nothing can be given as

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an approximation this is

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two three five

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and so on

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Let's get down to the solution means

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I'll designate how then all this

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equation turns into something

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like this take this that

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means, understand, the socks of the launch will be N A P

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plus Q from this equality it will be N

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cubed Let's now solve the system you can

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find P you can find Q I want to

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find Q for example, so here I'll write a minus sign

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from it from the second level 1 of the equation,

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which means PSP is abbreviated here remains Q

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minus Minus

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twice

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minus N

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then

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Q this will be

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in half Let's factorize the

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numerator, which means it will be

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in half This can also be factored in this

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will be

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one in half Let's now swap

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these numbers,

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look If you pay attention -1 + 1

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this is That

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is, three consecutive integers

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n -1 N and N + 1

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now And what can we say among three

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consecutive integers one

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is divisible by 3 by this two

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can be, as it were, reduced by some of

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these numbers Why Because among three

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consecutive numbers there will be some kind of

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multiple of 2

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means this whole equation will be a

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multiple of 3 Well, I’ll write it as three to

00:02:53

now

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on the left we have Q,

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from here

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we know that this is a prime number that is

00:03:04

divisible only by itself and by one without a

00:03:08

remainder,

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now among the prime numbers there are only 3

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is divided by three correctly we conclude

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Now if Q is equal to 3 we found out

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we need to find it

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cubed minus N in half it will be 3

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hence N cubed minus N it will be 6

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now And when this equation is satisfied

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Well let's substitute integers 0

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we substitute nothing happens then there is a

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solution has one substituting also 0

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two I'll put Let's Two in the Cube it

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will be 8 minus 2 it will be 6 means

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equal to 2 I found Let's look now

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this will be the

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solution means P equals 5

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Let's check

00:04:45

5 - 3 this is the 2nd not squared in the cube

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here I have a cube inside Two to the third

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power it will be 8 So the whole problem

00:04:56

is solved the answer n is 5 A Q is equal to 3

00:05:10

if there are other options for

00:05:13

solving methods You can write in the comments

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