It is proved by factorization that 257-512 can be divided by 120

It is proved by factorization that 257-512 can be divided by 120

It is proved that 257-512 = (52) 7-512 = 514-512 = 512 × (52-1) = 512 × 24 = 511 × 5 × 24 = 511 × 120, 257-512 can be divided by 120

If n is any integer, the value of (n + 11) ^ 2-N ^ 2 can always be divided by K, and the maximum value of K can be obtained

(n+11)^2-n^2
= (N+11+N)*(N+11-N)
= 11*(2N+11)
The constant factor of this factor is 11, so K has a maximum of 11

If n is any integer, the value of (n + 11) ^ 2-N ^ 2 can always be divided by K (k is not equal to 1)

（n+11）^2-n^2
=(n+11-n)(n+11+n)
=11(2n+11)
The constant factor is 11
So k = 11
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