The Fermat numbers are numbers of the form 2 ^2n + 1 = Φn . Prove that if n < m , then Φn │ϕ m - 2.

The Fermat numbers are numbers of the form 2 ^2n + 1 = (Phi)n . Prove that if n < m , then (Phi)n │(Phi)m - 2.

Solution Summary

This solution is comprised of a detailed explanation for solving the problems on Fermat numbers.
It contains step-by-step explanation for proving statement that if n < m , then Φn │Φm - 2,
where Φn is the Fermat numbers such that Φn = 2 ^2n + 1.
It contains step-by-step explanation for proving statement that if n < m , then (Phi)n │(Phi)m - 2,
where (Phi)n is the Fermat numbers such that (Phi)n = 2 ^2n + 1.

... 5) Use the above exercise to give a proof that there exist infinitely many primes. ... Posting 40184 reply 3 n 3) The Fermat numbers are numbers of the 2 2 + 1 ...

... Can you give mathematical proof for this ... case the argument above leading to Fermat's little theorem ... to remedy this problem by only considering numbers that have ...

... There is the following result for which Fermat's little theorem is a special ... Cambridge for proof ) ... is a finite field and 'r' is a 'prime' number, the number of ...

... A simple sketch of a proof goes as follows. ... common with 6 from 6). So, all the numbers 2^[(18 ... which includes a sketch of a derivation of Fermat's little theorem ...

We have learned Rolle, Lagrange, Fermat, Taylor Theorems in our ... 0) = 0 . Now we finished some preparation for the proof. ... 5 6 120 where θ is a number between 0 ...

... 3. Explain your solution process in words 4. Proofs need to be ... 3,7 and 13 are all prime numbers, we have ... Euler's theorem (also known as the Fermat-Euler theorem ...

... There are two proofs here, one regarding subgroups of the ... linear group and one involving prime numbers and modular ... b) This is known as Fermat's little theorem. ...

Context: We are learning Rolle, Lagrange, Fermat, Taylor Theorems in ... End of all proofs). ... carefully formatted and worked calculations to give the required proof. ...