Question

Prove that: For all integers n, 21| (3n^7 + 7n^3 + 11n). @MIT 18.01 Single …

Answer 1

it works for n=1
21|21
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assume it is true for some k
and now you have to show it is true for k+1

Answer 2

for some integer k*
for some integer l
21l=3k^7+7k^3+11k
now we want to show there is some integer m such that
21m=3(k+1)^7+7(k+1)^3+11(k+1)

Answer 3

See attached solution