From 78eda89b2d7e6456b6e02be57000a8dd74038fa0 Mon Sep 17 00:00:00 2001 From: "Robin P. Clark" Date: Tue, 7 Jul 2015 12:00:17 +0100 Subject: [PATCH] tidying subtitles --- papers/fermat/fermat.tex | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/papers/fermat/fermat.tex b/papers/fermat/fermat.tex index 987a75f..3da77e9 100644 --- a/papers/fermat/fermat.tex +++ b/papers/fermat/fermat.tex @@ -132,7 +132,7 @@ are lost and the $\prod cbpf(a,b)$ preserved. Because of this property of addition of numbers in relation to preserved prime factors, it can be used to make inferences on the equation $a^n+b^n = c^n$. % -\subsubsection{trivial example, single prime factor preserved} +\subsubsection{Trivial example, single prime factor preserved} % Consider $bpf(182)=\{2,7,13\}$ and $bpf(2365)=\{5,11,43\}$ these have no common prime factors so adding them should result in a number which when factored contains none of the primes in $182$ and $2365$. @@ -157,7 +157,7 @@ So, $ 322 + 49665 = 49987$: $bpf(49987) = \{7,37,193\}$. As expected the common prime factor,7, exists in the result of the addition but the uncommon prime factors have disappeared. -\subsubsection{trivial example, multiple prime factor preserved} +\subsubsection{Trivial example, multiple prime factor preserved} Consider a repeated prime factor (i.e. a prime $p$ to the power $t$ $p^t$). The same rules apply. % @@ -357,7 +357,7 @@ $$\prod \{2,2\} + \prod \{3,3,5,5,13,13,17,17\} = \{10989229\};$$ %$ans = 10989229 gives a larger prime number 10989229 and so on. -\subsection{fishing with cubic primes} +\subsection{Fishing with cubic primes} Fishing with primes cubed reveals larger primes quicker: take $$ \prod \{2,2,2,5,5,5,11,11,11\} + \prod \{3,3,3,7,7,7,13,13,13\} = \prod \{ 383 , 56599 \} \; ,$$ Adding 56599 as a single uncommon factor;