Recent content by mike1

yeah, I've got it now..thanks :)

Ignore...

Do you mean 0,3,0,3 and 0,1,0,1?

How do I compare it to that? Can I say since 3m^2=n^2+1, then 3m^2 is congruent to 0,1,2,3 mod(4)?...

Oh! So the remainders of 3m^2 are 0,3,0,3. So 3m^2 is congruent to 0 or 3 mod(4), but how we combine both of expressions?

Is it 0,1,4,9 but then times by 3 so 0,3,12,27? Or is that completely wrong..

Thanks :) For part b) Since n^2 is congruent to 0 or 1 mod(4), after re-arranging we see that 3m^2 = n^1+1, so then n^2 + 1 is congruent to 1 or 2 mod(4). What should be done about the 3m^2?

No, because 0/4 or 1/4 is not 2 or 3? & hence it's impossible to find an integer to satisfy it?

0= mod(4) 1= mod(4) 4= 0 mod(4) 9= 1 mod(4)

So: 9 = 1 mod(4), since 9-1 = 8/4=2

Sorry, still confused :(

Homework Statement Prove that it is impossible to find an integer n, such that n^2 = 2 mod(4) or n^2 = 3 mod(4) Hence or otherwise, prove that there do not exist integers m and n such that 3m^2 - 1 = n^2 Homework Equations The Attempt at a Solution Since n must be...

anyone?

A boat A is chasing boat B along a river by moving in the same direction as the stream. The speed of the river stream is 6 miles per hour, the speed of boat B relative to the river is 48 miles per hour, and boat A is 8 miles per hour slower than boat B. Currently boat B is ahead of boat A...