MathDB

Alice and Bob are playing "factoring game." On the paper,

270000(=2^43^35^4)

is written and each person picks one number from the paper(call it

N

) and erase

N

and writes integer

X,Y

such that

N=XY

and

\text{gcd}(X,Y)\ne1.

Alice goes first and the person who can no longer make this factoring loses. If two people use optimal strategy, prove that Alice always win.

Problem Statement