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A217551
Smallest numbers n, for a given s, such that s! + n^2 and (s+3)! + n^2 are squares.
3
1, 828, 508, 239499435, 4693095288000, 561589459200, 148245349824000
OFFSET
1,2
COMMENTS
The corresponding values of s are: 4, 8, 9, 15, 21, 24, 27.
EXAMPLE
4! + 1 = 5^2 and 7! + 1 = 71^2.
8! + 828^2 = 852^2 and 11! + 828^2 = 6372^2.
PROG
(PARI) for(n=4, 30, a=n!; b=((n+3)*(n+2)*(n+1)-1)*a; c=divisors(b); for(i=2, #c-1, s=c[i]; r=b\s; if(r<s, next(2), d=abs(s-r)/2; t=d^2-a; if(issquare(t), print([n, d, sqrtint(t)])))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Robin Garcia, Oct 06 2012
STATUS
approved