So far I've translated the A , B, C to plain English as I understand it but I believe there are mistakes.
A)
There exists a value a0 for the set of natural numbers where there exists a value d for the set of natural numbers ( in which d is greater than 0 and for all/each value k which belongs to a set of natural numbers for all/each value m which belongs to a set of natural numbers in which value m is true that in which a0 + value k times value j implies that value m is equal to 1 or value m is equal to value a0 + value k times d.
B)
For all / for each value p which belongs to a set of natural numbers there exists value a which belongs to a set of natural numbers in which P is Prime and not 2 such that value p implies that value a is not equal to 1 and a with the power of value p minus 1 divided by 2 is equivalent to 1 mod of value p.
C)
For all/for each value k which belongs to the set of natural numbers, in which k is greater or equal to 2 implies that for all values n which belong to a set of natural numbers that for all / for each value j which belongs to a set of natural numbers in which value j is less than value k it implies that for all/for each values m which belongs to a set of natural numbers in which 1 is less than value m or value m is less than value k which implies that not value m such that value n plus value j.
Maybe there is also a way to prove or disprove A, B and C statements?
A) There exist natural numbers $a_0$ and $d$ such that if each pair of natural numbers $k$ and $m$ is such that $m$ divides $a_0+kd,$ where $d$ is positive, then $m$ equals either $1$ or $a_0+kd.$
B) For each natural $p,$ there exists a natural $a$ such that if $2$ does not divide prime $p$ then $a^{\frac{p-1}2}$ is congruent modulo $p$ to, but $a$ does not equal, $1.$
Now try re-translating (C), using the ideas from my above translations.