Related Results
Fermat announced two related results fourteen years later. In a letter to Blaise Pascal dated September 25, 1654 he announced the following two results for odd primes :
He also wrote:
- If two primes which end in 3 or 7 and surpass by 3 a multiple of 4 are multiplied, then their product will be composed of a square and the quintuple of another square.
In other words, if p, q are of the form 20k + 3 or 20k + 7, then pq = x2 + 5y2. Euler later extended this to the conjecture that
Both Fermat's assertion and Euler's conjecture were established by Lagrange.
Read more about this topic: Fermat's Theorem On Sums Of Two Squares
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