# maths

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prove by mathematical induction that 7n+4n+1 is divisible by 6

• maths - error -

As written, it's obviously false. Try n=2
Did you mean 7n^2+4n+1? Nope; false for n=2

Got some error here

• maths -

its 7^n+4^n+1

• maths -

Steve

• maths -

Ah; that's a lot nicer.

it's true for n=1.
So, assume it's true for n=k.

7^(k+1) + 4^(k+1) + 1
= 7*7^k + 4*4^k + 1
= (1+6)*7^k + (1+3)*4^k + 1
= (7^k+4^k+1) + 6*7^k + 3*4^k

obviously, 6*7^k is divisible by 6
4^k is even, so 3*4^k is divisible by 6
So, since we're adding three items which are all multiples of 6, the whole is a multiple of 6.

Thus, the induction step holds.

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