I've edited the original question because there was a mistake in it.
can x and y be determined if it is given that there are 65 values which the sum a multiple of x and a multiple of y cannot give
I.e. Nx + My has 65 unattainable values, where N and M are variables. Also x and y both do not equal 2.
I saw it on: Hard math questions, again? - Yahoo! Answers
Its the last part to the last question.
hi thanks, so the reasoning is we can't solve it because we don't know if c is the greatest common divisor of a and b?
But i thought that is just the case if we want to have infinite solutions?
i.e. with pentagonal square numbers would have infinite integer solutions, right?
Pentagonal Square Number -- from Wolfram MathWorld
It suffices if gcd(M,N) divides 65 to have infinite solutions, else it wont have any solution...
To see this observe that if gcd(M,N) does not divide 65 and there exists a solution, then gcd(M,N) divides the left hand side, but not the right hand side...
If it does divide, then use division algorithm to solve for . Let be one solution and then generate for various t, to get infinite solutions.
Ah right, I think I'll make a new thread for the Pell's Equations then lol
Anyways, did u just edit your previous post because this wasnt there before (i think)
To see this observe that if gcd(M,N) does not divide 65 and there exists a solution, then gcd(M,N) divides the left hand side, but not the right hand side...
If it does divide, then use division algorithm to solve for . Let be one solution and then generate for various t, to get infinite solutions.
I havent done algorithms (sorry ) could you explain that paragraph if you dont mind?
oops i just realised im doing the question wrong...
It is actually:
can x and y be determined if it is given that there are 65 values which the sum a multiple of x and a multiple of y cannot give
I.e. Nx + My has 65 unattainable values, where N and M are variables. Also x and y both do not equal 2.
I saw it on: Hard math questions, again? - Yahoo! Answers
Its the last part to the last question.
I think this requires the chicken mcnugget theorem
but i'm not sure how to use it. any ideas?
Chicken McNugget Theorem - AoPSWiki