Difference between revisions of "2000 JBMO Problems/Problem 2"
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Thus <math>n = 1</math> or <math>3</math>. | Thus <math>n = 1</math> or <math>3</math>. | ||
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Revision as of 23:48, 12 March 2023
Problem 2
Find all positive integers such that
is the square of an integer.
Solution
After rearranging we get:
Let
we get:
or,
Now, it is clear from above that divides
. so,
If
so
But
If then
increases exponentially compared to
so
cannot be
.
Thus .
Substituting value of above we get:
or this results in only
or
Thus or
.
~Kris17