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Difference between revisions of "2007 iTest Problems/Problem 20"

(Created page with "== Problem == Find the largest integer <math>n</math> such that <math>2007^{1024}-1</math> is divisible by <math>2^n</math> <math>\text{(A) } 1\qquad \text{(B) } 2\qquad \text...")
 
m (→‎Problem)
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\text{(F) } 6\qquad
 
\text{(F) } 6\qquad
 
\text{(G) } 7\qquad
 
\text{(G) } 7\qquad
−
\text{(H) } 8\qquad \\ </math>
+
\text{(H) } 8\qquad</math>
 
<math>\text{(I) } 9\qquad
 
<math>\text{(I) } 9\qquad
 
\text{(J) } 10\qquad
 
\text{(J) } 10\qquad
Line 19: Line 19:
 
\text{(N) } 14\qquad
 
\text{(N) } 14\qquad
 
\text{(O) } 15\qquad
 
\text{(O) } 15\qquad
−
\text{(P) } 16\qquad \\ </math>
+
\text{(P) } 16\qquad</math>
 
<math>\text{(Q) } 55\qquad
 
<math>\text{(Q) } 55\qquad
 
\text{(R) } 63\qquad
 
\text{(R) } 63\qquad

Revision as of 17:08, 10 June 2018

Problem

Find the largest integer $n$ such that $2007^{1024}-1$ is divisible by $2^n$

$\text{(A) } 1\qquad \text{(B) } 2\qquad \text{(C) } 3\qquad \text{(D) } 4\qquad \text{(E) } 5\qquad \text{(F) } 6\qquad \text{(G) } 7\qquad \text{(H) } 8\qquad$ $\text{(I) } 9\qquad \text{(J) } 10\qquad \text{(K) } 11\qquad \text{(L) } 12\qquad \text{(M) } 13\qquad \text{(N) } 14\qquad \text{(O) } 15\qquad \text{(P) } 16\qquad$ $\text{(Q) } 55\qquad \text{(R) } 63\qquad \text{(S) } 64\qquad \text{(T) } 2007\qquad$

Solution

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