Answer to puzzle 58: Fifth power plus five
n5 + 5 and (n + 1)5 + 5 are relatively prime only if n 
533360 (mod 1968751).
If n = 533360 (mod 1968751), their greatest common divisor is 1968751.
n5 + 5 and (n + 1)5 + 5 are relatively prime only if n 533360 (mod 1968751).
If n = 533360 (mod 1968751), their greatest common divisor is 1968751.