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:
“In the middle years of childhood, it is more important to keep alive and glowing the interest in finding out and to support this interest with skills and techniques related to the process of finding out than to specify any particular piece of subject matter as inviolate.”
—Dorothy H. Cohen (20th century)
“We do not raise our children alone.... Our children are also raised by every peer, institution, and family with which they come in contact. Yet parents today expect to be blamed for whatever results occur with their children, and they expect to do their parenting alone.”
—Richard Louv (20th century)