Number Theory
Mersenne Numbers
Mersenne Numbers \[\begin{array}{l} We\;now\;giving\;a\;method\;for\;finding\;large\;prime\;numbers,\;w…
Mersenne Numbers \[\begin{array}{l} We\;now\;giving\;a\;method\;for\;finding\;large\;prime\;numbers,\;w…
\[\begin{array}{l} The\;quadratic\;congruence\;\;{x^2} + 1 \equiv 0\;(modp),where\;p\;is\;an\;odd\;pri…
Proof that If the prime p divides Fm, where m ≥ 2, then p = k 2^(m+2)+1 for some positive integer k. …
\[\begin{array}{l}\\ Modulo\;4,\;\;we\;have\;four\;possible\;remainders\;\\\\ a = 0,1,2,\;\;or\;3\;for\…
\[\begin{array}{l} Suppose\;that\;{F_n}\;and\;{F_{n + k}},{\rm{ }}where,\;are\;two\;Fermat\;numbers,\;a…
\begin{array}{l}\\ {F_6} = {2^{64}} + 1 = {2^{48}} * {2^{16}} + 1\\\\ = 281474976710656 * {2^{16}} + 1\\…
\[\begin{array}{l} {F_5} = {2^{{2^5}}} + 1 = 4294967297\\\\ The{\rm{ }}Fermat{\rm{ }}number\;{F_5}\;is{\r…