Hello, need your help thanks.

Find all positive integers satisfying simultaneously two conditions.

i) is a rational number .

ii) is a prime .

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- Apr 21st 2009, 05:15 AMmaria18Find positive integers
Hello, need your help thanks.

Find all positive integers satisfying simultaneously two conditions.

i) is a rational number .

ii) is a prime . - Apr 21st 2009, 05:54 AMShowcase_22

but since y has to be an integer, then and where .

I'm not sure how this helps =S - Apr 21st 2009, 07:15 AMSoroban
Hello, maria18!

I found something, but I too haven't solved it yet.

Quote:

Find all positive integers satisfying simultaneously two conditions:

is a rational number.

is a prime.

Rationalize: . .

. . . . . . . . .

Since is an integer: .

Can we exploit that fact? . . . I don't know.

- Apr 21st 2009, 12:10 PMMoo
- Apr 22nd 2009, 08:09 AMmaria18
- Apr 22nd 2009, 08:15 AMShowcase_22
Thanks Moo for pointing that out.

This question is actually harder than it looks!

can only be prime if only one of the expressions in the brackets is 1.

ummm....... (Headbang) - Apr 22nd 2009, 03:25 PMmaria18
- Apr 22nd 2009, 03:37 PMShowcase_22
You can use that to find all the other integers though can't you?

(I haven't tried it myself, but by substituting them into the equationswe can obtain values for x and z. They're going to be different depending on the y value).