Problem $4.$ You are secretly eavesdropping on a top secret conversation between two spies, Alice

and Bob. Alice has secretly picked an integer $n,$ while Bob has secretly picked an

integer $m.$ You know that Alice and Bob have chosen the prime $p=101$ and $g=88$

as the public key. You hear Alice tell Bob that $39-=ng(mod101),$ and you hear Bob

tell Alice that $75-=mg(mod101).$

$($a$)$ Find Alice's secret key $n(mod101).$

$($b$)$ Find Bob's secret key $m(mod101).$

$($c$)$ Find Alice and Bob's shared secret key $s=nmg(mod101).$

Please type and show all steps to each part of the problem.