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**1. Homework Statement**

show that for all natural numbers n: 3^(2n+1)+2^(n-1) is divisible by 7

**3. The Attempt at a Solution**

i've been trying to get the second part of the proof to look like the first part, so as to be able to conclude some multiple is also divisible by 7, but i don't seem to get what needs to be done..

3^(2(n+1)+1)+2^(n+1-1)

**->**3^(2n+2+1)+2^(n+1-1)

**->**3²*3^(2n+1)+2*2^(n-1) (= 7*k)

only here i sort of get stuck trying to get the multipliers out, and i'm not certain enough of my math 'certain knowledge' otherwise to just posit that 3*(something)+2*(something) always yields multiples of 7 (not that it does, in this case)

am i really trying to go down the wrong path here? or am i just missing something entirely too obvious? :(