3^4n+1 + 2^ 2n+2 is divisible by 7

P(n): 34n+1+22n+2 is divisible by 7
step 1: let n=1
                    34+1+16=243+16=259 is divisible by 7
step 2: let n=k and let P(n) is true for n=k.
                    34k+1+22k+2=7m
                    34k+1=7m-22k+2    -(1)
step 3: let n=k+1
                    34k+5+22k+4
                    34k+1.34+22k+4
                    (7m-22k+2)81+22k+4    [ from equation (1) ]
                    567m-81.22k+2+22k+4
                    567m-22k+2(81-4)
                    567m-22k+2(77)
                    7[ 81m-22k+2(11) ]
          P(k+1) is true because P(k) is true
Hence P(n) is true for all natural numbers
  • 8
This question no 24 can anyone solve

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