G********t
发帖数: 334 | 1 what is the greatest integer that divides p^4-1 for every prime number
greater than 5?
thanks very much!! |
C********n
发帖数: 6682 | 2 240?
【在 G********t 的大作中提到】
: what is the greatest integer that divides p^4-1 for every prime number
: greater than 5?
: thanks very much!!
|
C********n
发帖数: 6682 | 3 p=2n+1
p^4-1 = (2n+1)^4-1 =((2n+1)^2 +1)((2n+1)^2 -1)
== 8(2n*(n+1) +1 )*n*(n+1)
easy to see this one could be divided by 16
also n cant be 3m+1, check n=3n or 3n+2 to see P^4-1 can be divided by 3
same, n cant be 5m+2 , check rest to make sure P^4 -1 mod 5 =0
and for 7^4-1 the factors are 2 2 2 2 3 5 61
so 16*3*5 == 240, final answer
【在 G********t 的大作中提到】
: what is the greatest integer that divides p^4-1 for every prime number
: greater than 5?
: thanks very much!!
|
f**l
发帖数: 2041 | 4 240? 16*3*5
【在 G********t 的大作中提到】
: what is the greatest integer that divides p^4-1 for every prime number
: greater than 5?
: thanks very much!!
|
