For what each time value of n in this expression 3^4n -4^3n is exactly divisible by 17

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Solution

3^4n - 4^3n
put n =1
3^4 -4^3 = 81-64=17

now put n=2
3^8-4^6 =6561-4096= 2465 =17*145

similarly for all n= 1 2 3 .. .....
it is divisible by 17

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