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Question

Show that 34n+2+52n+1 is a multiple of 14.

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Solution

f(n)=34n+2+52n+1f(1)=34+2+52+1=729+125=854=14×61

which is a multiple of 14

f(n+1)=34n+6+52n+3f(n+1)25f(n)=34n+6+52n+325(34n+252n+1)f(n+1)f(n)=34n+625.34n+2+52n+325.52n+1f(n+1)f(n)=34n+2(8125)+52n+352n+3f(n+1)f(n)=56.34n+2

which is also a multiple of 14

Hence proved.


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