Prime Number's Haunting Me!!!
Number Theory
Level
pending
P is a member of Prime Number, Q is a Prime Number.
How much member of P that can complete this problem?
More than 2
2
1
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1 solution
For P>3, 2^P=-1 MOD 3 and P^2=1 MOD 3. So for P>3, 2^P+P^2=0 MOD 3, so no solutions for P>3. When P=2, we get 8=2^3. When P=3, we get 17, which is a solution. Hence only 1 solution.