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Add 1 to Exponent*Number, Get Square (Posted on 2023-07-02)

Determine all possible values of a nonnegative integer n such that;

• 2^n-1*n +1 is a perfect square.

Note: Adapted from a problem which appeared in a Georgia IMO.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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computer findings

| Comment 1 of 2

digits 300

clearvars,clc

for n=vpa(0):450

v=2^(n-1)*n+1;

sr=round(sqrt(v));

if sr*sr==v

disp([n v sr])

end

finds only

[0, 1, 1]

[5.0, 81.0, 9]

for the [n, formula value, square root].

Posted by Charlie on 2023-07-02 10:09:16

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