Let nnn be an integer. For what values of nnn is n4+n2+1n^4 + n^2 + 1n4+n2+1 divisible by 131313?
n≡2,6,7,11(mod13)n \equiv 2, 6, 7, 11 \pmod{13}n≡2,6,7,11(mod13)
n≡1,5,8,12(mod13)n \equiv 1, 5, 8, 12 \pmod{13}n≡1,5,8,12(mod13)
n≡3,4,9,10(mod13)n \equiv 3, 4, 9, 10 \pmod{13}n≡3,4,9,10(mod13)
No such nnn exists