A Nice Math Olympaid Exponential Equation | How to Solve for "k" #math #algebra
Пікірлер: 10
@michaeledwards2251Ай бұрын
For a difference of 2059, factors 71 and 29, for k=7, the solution is a matter of substitution.
@user-ji5su2uq9mАй бұрын
1) Why don't you try for x+y=65, x-y=1(actually no integer solution.) 2) You must show k is even. otherwise x=3^(k/2) and y=2^(k/2) are not integers. [Proof] 3^k - 2^k = 65 => 0 - 2^k ≡ 2 (mod 3) => 2^k ≡ 1 (mod 3) => k is even.
If the difference was 211, a prime number, for k =5, how would the problem be solved ? For a difference of 665, factors, 5, 7 and 19, for k =6, the methodology should work.