SANSKAR'S OG PROBLEMS
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Problem1
Let be a 2-digit positive integer satisfying
=
. Find
.
Solution 1 by ddk001
we have
Obviously, the left increase much slower for big and
so
and
must be small. (Namely,
)
don't work so
, so since
, the max of
is
, which didn't work so
. since the max now would be
, and that doesn't work, the max is now
, which is not a 2-digit integer. Hence, no such ordered pair
exist. ~Ddk001
Problem2
For any positive integer ,
>1 can
be a perfect square? If yes, give one such
. If no, then prove it.