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
Famous quotes containing the words related and/or results:
“No being exists or can exist which is not related to space in some way. God is everywhere, created minds are somewhere, and body is in the space that it occupies; and whatever is neither everywhere nor anywhere does not exist. And hence it follows that space is an effect arising from the first existence of being, because when any being is postulated, space is postulated.”
—Isaac Newton (1642–1727)
“A distinction of property results from that very protection which a free Government gives to unequal faculties of acquiring it.”
—James Madison (1751–1836)