perplexus.info :: Numbers : Consider Prime Numbers, Get Cube

Consider Prime Numbers, Get Cube (Posted on 2023-10-24)

Determine all possible values of a prime number p, such that:

p²-p+1 is a perfect cube.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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computer solution

| Comment 1 of 7

p=primes(99999999);

for i=1:length(p)

c=p(i)^2-p(i)+1;

cr=round(c^(1/3));

if cr^3==c

disp([p(i) c cr])

end

tests all primes below 100 million and finds only p = 19, p^2 - p + 1 = 343, which is 7^3.

Posted by Charlie on 2023-10-24 08:49:46

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