\(\displaystyle{a}\equiv{99}{\left({b}\text{mod}{41}\right)}\)
We can find a such that
\(\displaystyle{100}\leq{a}\leq{140}\)
by consecutively adding 41 to 99 until we ibtain a vlue between 100 and 140
\(\displaystyle{a}\equiv{99}{\left({b}\text{mod}{41}\right)}\)

\(\displaystyle\equiv{99}+{41}{\left({b}\text{mod}{41}\right)}\)

\(\displaystyle\equiv{140}{\left({b}\text{mod}{41}\right)}\) Since between 100 and 140 (including): a=140

\(\displaystyle\equiv{99}+{41}{\left({b}\text{mod}{41}\right)}\)

\(\displaystyle\equiv{140}{\left({b}\text{mod}{41}\right)}\) Since between 100 and 140 (including): a=140