MathDB

8

Part of 2021 AMC 10 Fall

Problems(2)

cuddly numbers

Source: 2021 AMC 10A #8

11/11/2021
A two-digit positive integer is said to be cuddly if it is equal to the sum of its nonzero tens digit and the square of its units digit. How many two-digit positive integers are cuddly?
<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>1<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>3<spanclass=′latex−bold′>(E)</span>4<span class='latex-bold'>(A) </span>0\qquad<span class='latex-bold'>(B) </span>1\qquad<span class='latex-bold'>(C) </span>2\qquad<span class='latex-bold'>(D) </span>3\qquad<span class='latex-bold'>(E) </span>4
Mersenne non-prime

Source: 2021 Fall AMC10B P8/AMC10B P6

11/17/2021
The largest prime factor of 1638416384 is 22, because 16384=21416384 = 2^{14}. What is the sum of the digits of the largest prime factor of 1638316383?
<spanclass=′latex−bold′>(A)</span>3<spanclass=′latex−bold′>(B)</span>7<spanclass=′latex−bold′>(C)</span>10<spanclass=′latex−bold′>(D)</span>16<spanclass=′latex−bold′>(E)</span>22<span class='latex-bold'>(A) </span>3\qquad<span class='latex-bold'>(B) </span>7\qquad<span class='latex-bold'>(C) </span>10\qquad<span class='latex-bold'>(D) </span>16\qquad<span class='latex-bold'>(E) </span>22
AMCAMC 10AMC 10 BAMC 12AMC 12 B