A place to air possible concerns or difficulties in understanding ProjectEuler problems. This forum is not meant to publish solutions. This forum is NOT meant to discuss solution methods or giving hints how a problem can be solved.
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Problem 784
I'm having big trouble understanding problem 784, am I the only one ?
Let's call a pair of positive integers $p$, $q$ ($p \lt q$) <i>reciprocal</i>, if there is a positive integer $r\lt p$ such that $r$ equals both the inverse of $p$ modulo $q$ and the inverse of $q$ modulo $p$.
For example, $(3,5)$ is one reciprocal pair for $r=2$.
I really don't understand this sentence, can someone elaborate the meaning ?
In the literal sense, for me, 3 modulo 5 = 3 and 5 modulo 3 = 2, the inverse of these numbers is not 2.
Problem 784
I'm having big trouble understanding problem 784, am I the only one ?
Let's call a pair of positive integers $p$, $q$ ($p \lt q$) <i>reciprocal</i>, if there is a positive integer $r\lt p$ such that $r$ equals both the inverse of $p$ modulo $q$ and the inverse of $q$ modulo $p$.
For example, $(3,5)$ is one reciprocal pair for $r=2$.
I really don't understand this sentence, can someone elaborate the meaning ?
In the literal sense, for me, 3 modulo 5 = 3 and 5 modulo 3 = 2, the inverse of these numbers is not 2.
You misunderstood the meaning of the word "inverse". It means the multiplicative inverse. In the example, it means that $2\equiv3^{-1} \bmod 5$, and $2\equiv5^{-1} \bmod 3$ are both true (or equivalently $2\cdot3\equiv1 \bmod 5$, and $2\cdot5\equiv1 \bmod 3$ are both true).
