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tidying subtitles

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Robin P. Clark 2015-07-07 12:00:17 +01:00
parent 6de870f7c7
commit 78eda89b2d
1 changed files with 3 additions and 3 deletions
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papers/fermat/fermat.tex
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@ -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;