2007 iTest Problems/Problem 24

Problem

Let $N$ be the smallest positive integer such that $2008N$ is a perfect square and $2007N$ is a perfect cube. Find the remainder when $N$ is divided by $25$ .

$\text{(A) }0 \quad \text{(B) }1 \quad \text{(C) }2 \quad \text{(D) }3 \quad \text{(E) }4 \quad \text{(F) }5 \quad \text{(G) }6 \quad \text{(H) }7 \quad \text{(I) } 8\quad \$ (Error compiling LaTeX. Unknown error_msg)

$\text{(J) }9 \quad \text{(K) }10 \quad \text{(L) }11 \quad \text{(M) }12 \quad \text{(N) }13 \quad \text{(O) }14 \quad \text{(P) }15 \quad \text{(Q) }16 \quad \$ (Error compiling LaTeX. Unknown error_msg)

$\text{(R) }17 \quad \text{(S) }18 \quad \text{(T) }19 \quad \text{(U) }20 \quad \text{(V) }21 \quad \text{(W) }22 \quad \text{(X) }23$

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2007 iTest Problems/Problem 24

Problem

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