diff --git a/papers/fermat/fermat.tex b/papers/fermat/fermat.tex
index 5e2a06a..2d1c033 100644
--- a/papers/fermat/fermat.tex
+++ b/papers/fermat/fermat.tex
@@ -125,10 +125,12 @@ Thus only common prime factors in $a$ and $b$ are   preserved
 as a result of equation~\ref{eqn:primesexpanded1}.
 This is simply because in addition
 the common prime factors can be extracted, $a+b \equiv \prod bfp(a) + \prod bfp(b)$
-re-writing $\prod cbpf(a,b) \big( \prod ubpf(a) + \prod ubpf(b) \big)$:
-This means the uncommon prime factors of $\big( \prod ubpf(a) + \prod ubpf(b) \big)$
+extracting the common prime factors this becomes $\prod cbpf(a,b) \big( \prod ubpf(a) + \prod ubpf(b) \big)$:
+this means the uncommon prime factors of $\big( \prod ubpf(a) + \prod ubpf(b) \big)$
 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 $a^n+b^n = c^n$.
 %
 %
 This means for $a+b$ and $a^n+b^n$ the only prime factors  preserved (i.e. in $c^n$)
@@ -218,7 +220,7 @@ If $a$ and $b$ are whole numbers they either create a result with
 the highest prime more than once, or it is destroyed by addition.
 
 For $a^n + b^n = c^n$, for the highest prime, this means $a+b=1$.
-This means that where $a$ and $b$ are $ > 2$; $a^n + b^n \neq c^n$ for whole numbers.
+This means that where $a$ and $b$ are $ > 1$; $a^n + b^n \neq c^n$ for whole numbers.
 This concept can be extended to numbers where there are duplicate highest primes.
 
 
@@ -245,7 +247,7 @@ so that $a p^{tn} + b p^{tn} = p^{tn} $ satisfy the highest prime in $c$.
 %
 In order for this to be true $a$ and $b$ must both be fractions of a whole number:
 again this means $a+b$ must equal 1.
-Thus where $a$ and $b$ are $ > 2$; $a^n + b^n \neq c^n$ for whole numbers.
+Thus where $a$ and $b$ are $ > 1$; $a^n + b^n \neq c^n$ for whole numbers.
 
 \subsection{trivial case}