turkey-yks 2013 Q6

turkey-yks · Other · lys1-math Number Theory Prime Number Properties and Identification

a, b are positive integers, p is a prime number and
$$a ^ { 3 } - b ^ { 3 } = p$$
Given this, which of the following is the equivalent of $a ^ { 2 } + b ^ { 2 }$ in terms of $p$?
A) $\frac { p + 1 } { 2 }$
B) $\frac { p + 3 } { 2 }$
C) $\frac { p + 2 } { 3 }$
D) $\frac { 2 p - 1 } { 2 }$
E) $\frac { 2 p + 1 } { 3 }$

a, b are positive integers, p is a prime number and

$$a ^ { 3 } - b ^ { 3 } = p$$

Given this, which of the following is the equivalent of $a ^ { 2 } + b ^ { 2 }$ in terms of $p$?\\
A) $\frac { p + 1 } { 2 }$\\
B) $\frac { p + 3 } { 2 }$\\
C) $\frac { p + 2 } { 3 }$\\
D) $\frac { 2 p - 1 } { 2 }$\\
E) $\frac { 2 p + 1 } { 3 }$

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