2007 iTest Problems/Problem 20
Problem
Find the largest integer such that
is divisible by
Solution
The expression can be factored by repeatedly using the difference of squares.
Notice that
, so
. Thus, in the expression
, if
is even, then the expression is congruent to
modulo
.
The remaining numbers to consider are and
. Factoring
yields
, and factoring
yields
.
That means has
as the exponent of
, so the largest
that makes
a factor of
is
.
See Also
2007 iTest (Problems) | ||
Preceded by: Problem 19 |
Followed by: Problem 21 | |
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