Let $a_n=6^{n}+8^{n}$. Determine the remainder upon dividing $a_ {83}$ by $49$.
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Problem Statement Let $x$ and $y$ be two-digit integers such that $y$ is obtained by reversing the digits of $x$. The integers $x$ and $y$ satisfy $x^2 - y^2 = m^2$ for some positive integer $m$....
Problem Statement (a) First, determine two positive integers $x$ and $y$ with $\dfrac{2x + 11y}{3x + 4y} = 1$. Now, let $u$ and $v$ be two positive rational numbers with $u<v$. If we write $u...
Problem Statement The polynomial $1-x+x^2-x^3+\cdots+x^{16}-x^{17}$ may be written in the form $a_0+a_1y+a_2y^2+\cdots +a_{16}y^{16}+a_{17}y^{17}$, where $y=x+1$ and the $a_i$’s are constants. F...
AIME 1986 P11
AIME 1999 P3
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