Question

show that \(\large k^7/7 + k^5/5 + 2k^3/3 -k/105\) is an integer for all nonnegative integer values of \(k\)

Answer 1

multiple of 105 eh

Answer 2

\[k^7/7 + k^5/5 + 2k^3/3 -k/105\\
(15k^7 + 21k^5 + 70k^3 -k)=105*y\\
k(15k^6 + 21k^4 + 70k^2 -1)=105*y\]

maybe we gotta show this is true

(15k^6 + 21k^4 + 70k^2 -1) = 0 mod 105

Answer 3

ah no that k is vital

Answer 4

(15k^7 + 21k^5 + 70k^3 -k) = 0 mod 105