When 3³⁷ is divided by 80, the remainder is

We have,

$3^{37}=3^{4.9}\cdot 3=3(81{)}^9=3(80+1{)}^9$

$=3{(}^9{\mathrm{C}}_0\cdot {80}^9{+}^9{\mathrm{C}}_1{80}^8+\dots {+}^9{\mathrm{C}}_9)$

Thus, when 3³⁷ is divided by 80, then the remainder is 3.