Please help me with this question from Cambridge 3u yr 11. (Pg 235 4b)
Question:
Prove these divisibility results, advancing in part B of the proof from k to k + 2:
(b) For odd n: (i) 3^n + 7^n is divisible by 10
I have done all the way to proving 3^(k+2) + 7^(k+2) = 10p, where p is an integer.
LHS = 3^k × 3^2 + 7^k × 7^2
Now I'm really stuck as to getting 3^k + 7^k from this. If anyone of you math geniuses help me out here, then I could do the rest of these 'odd' questions. Thank you so much
Question:
Prove these divisibility results, advancing in part B of the proof from k to k + 2:
(b) For odd n: (i) 3^n + 7^n is divisible by 10
I have done all the way to proving 3^(k+2) + 7^(k+2) = 10p, where p is an integer.
LHS = 3^k × 3^2 + 7^k × 7^2
Now I'm really stuck as to getting 3^k + 7^k from this. If anyone of you math geniuses help me out here, then I could do the rest of these 'odd' questions. Thank you so much