Try this beautiful problem from the PRMO, 2019 based on Rational Number and Integer.
let the rational number \(\frac{p}{q}\) be closest to but not equal to \(\frac{22}{7}\) among all rational numbers with denominator < 100, find p-3q.
Rational number
Algebra
Integer
Answer: is 14.
PRMO, 2019, Question 9
Higher Algebra by Hall and Knight
|\(\frac{22}{7}-\frac{p}{q}\)|=|\(\frac{22q-7p}{7q}\)| then |22q-7p|=1 for smallest value
and q=99 then p=311
p-3q=311-(3)(99)=311-297=14.
