Prove by mathematical induction that 7^(2n) - 48n - 1 is a multiple of 2304

I am ok with the first and second steps, but I am confused with the third i.e. when substituting n = k + 1.

Any help please?

Thanks a lot

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- Feb 28th 2010, 10:50 AMyobaculMathematical Induction
Prove by mathematical induction that 7^(2n) - 48n - 1 is a multiple of 2304

I am ok with the first and second steps, but I am confused with the third i.e. when substituting n = k + 1.

Any help please?

Thanks a lot - Feb 28th 2010, 11:18 AMJhevon
- Feb 28th 2010, 11:51 AMArchie Meade
hi yobacul,

**F(n)**

is a multiple 2304 ?

**F(k+1)**

is a multiple of 2304 if the "k"th term is ?

Does the hypothesis F(n)__cause__this to be true ?

Now express -48k as a multiple of

To do this we need to subtract another 48(48k)

{and therefore also add that amount}

The final term is

therefore, the term-by-term link is established.

Hence, if F(n) is valid, F(n+1) also is