Using induction, prove that for every positive integer $n$, there exists an integer $x_n$ such that $$x_n^2 \equiv 14 \mod 5^n$$
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Second page
I really need help with this problem as I'm doing a basic mathematical induction course and the professor did a pretty horrid job at explaining this problem. I also asked four other TA's (teaching assistants) and only one of them was able to explain it but they used the Jacobi symbol, a concept we haven't learned.
PS: if someone can help with the formatting of this question I'd greatly appreciate it as I'm relatively new to this site.