January+17

Question 1

Find all integer solutions of the equation 65432 x + 98765 y = gcd(65432,98765)

Question 2

Show that math \gcd(10^n-1,10^m-1)=10^{\gcd(m,n)}-1 math for any natural numbers m,n.

Question 3 --- Notice the correction! (instead of a, we now have ab)

Find an integer solution of math a^2+ab+b^2=3c^2 math with a>1000 and with a, b, c having no common factor.