Solve the equation for integers:

.

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- May 15th 2008, 06:50 AMjames_bondSolve the equation
Solve the equation for integers:

. - May 15th 2008, 06:58 AMives
by guessing.....................lol'

x=4,y=2

want to get an integer, so y should be multiple of 2, so i like 2..... - May 15th 2008, 08:00 AMSoroban
Hello, james_bond!

Quote:

Solve the equation for integers: .

Since the right side is rational, the exponent must be an integer.

. . Hence, the right side is a power-of-2.

Then: . for some positive integer

. . And: .

So must be divisible by 3.

. . This happens when is even: .

. . Hence, we have: .

Then [1] becomes: .

. . and we have: .

Substitute [2] into [3]: .

Solution: .

The first few solutions are: .