All odd numbers can be expressed as the square difference of two natural numbers

All odd numbers can be expressed as the square difference of two natural numbers

Proof: because
N^2-(N-1)^2
= N^2-(N^2-2N+1)
= N^2-N^2+2N-1
= 2N-1
Namely
2N-1
= N^2-(N-1)^2
The proof is complete

All odd numbers can be regarded as the square difference of two natural numbers

The proof is as follows:
Let K be any natural number, then
(k+1)²-k²=k²+2k+1-k²=2k+1
K is a natural number, then 2K + 1 can be expressed as any odd number!
So any odd number 2K + 1 is equal to the square difference between (K + 1) and K
That is to say, all odd numbers can be regarded as the square difference of two natural numbers
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Can all even numbers be expressed as the square difference of two natural numbers?
To prove

Let even number a = M & # 178; - N & # 178; (M and N are both natural numbers) a = (M + n) (m-n) / square difference formula m + N and M-N are odd or even. If the product is even, only m + N and M-N are even. M and N are even or odd (because if M and N are odd and even, then sum and difference are odd). If M and N are even, let m = 2p

The greatest common factor of two continuous natural numbers is 1, and the least common multiple is 56. These two numbers are () and（
The greatest common factor of two continuous natural numbers is 1, and the least common multiple is 56. These two numbers are () and (). Thank you

Hello
The greatest common factor of two continuous natural numbers is 1, and the least common multiple is 56. These two numbers are (7) and (8)

A = 56, (both a and B are natural numbers that are not zero), the least common multiple of a and B is (), and their greatest common factor is

Least common multiple: 56
Greatest common factor: 1

There are two different natural numbers whose products are 56 and 18

56=7×8=4×14=2×28
Only 4 × 14 (4 + 14 = 18)
Their difference = 14-4 = 10

A natural number minus 45 is a perfect square number. If the natural number plus 44 is still a perfect square number, then the natural number is a perfect square number______ ．

Let the number be x, then x-45 is a complete square number, and X + 44 is a complete square number, so the difference between the two complete square numbers is 2K + 1 = x + 44 - (x-45), that is, k = 44, so x-45 is the square of 44, and X + 44 is the square of 45, so the number is 1981. So the answer is: 1981

The squares of natural numbers are arranged from small to large into 1491623649 What is the 100th digit from left to right?

36*36=1296
It's nine

The squares of natural numbers are arranged in order of magnitude 1491623649 & nbsp Q: what is the number of position 612?

The square of 1-3 is one digit, occupying 3 positions; the square of 4-9 is two digit, occupying 12 positions; the square of 1o-31 is three digit, occupying 66 positions; the square of 32-99 is four digit, occupying 272 positions; the square of 1-99 is arranged in a row, occupying 3 + 12 + 66 + 272 = 353 positions, from 612-353 =

There is a natural number whose sum with 64 is exactly equal to the square of a certain number, and whose sum with 100 is exactly equal to the square of another number. What is the number?

Let this number X
Then x + 64 = a ^ 2
x+100=b^2
The latter formula minus the former formula has b ^ 2-A ^ 2 = 36
That is, (B-A) (B + a) = 2 × 2 × 3 × 3
Therefore, the values of B-A and B + A may be 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6
Only 2 and 18 have integer solutions, and a is 8, B is 10
When we substitute the first two equations, we have x = 0
That is, the number is 0