MathDB

9

Part of 2018 MIG

Problems(2)

2018 Individual #9

Source:

5/6/2022
Define f(x)=x2+5f(x) = x^2 + 5. Find the product of all xx such that f(x)=14f(x) = 14.
<spanclass=′latex−bold′>(A)</span>−9<spanclass=′latex−bold′>(B)</span>−3<spanclass=′latex−bold′>(C)</span>0<spanclass=′latex−bold′>(D)</span>3<spanclass=′latex−bold′>(E)</span>9<span class='latex-bold'>(A) </span>{-}9\qquad<span class='latex-bold'>(B) </span>{-}3\qquad<span class='latex-bold'>(C) </span>0\qquad<span class='latex-bold'>(D) </span>3\qquad<span class='latex-bold'>(E) </span>9
2018 Individual
2018 Team #9

Source:

1/18/2023
A certain 44 digit prime number has all prime digits. When any one of the digits is removed, the remaning three digits form a composite number in their initial order (i.e. if 12341234 were the answer, then 123123, 234234, 134134, and 124124 would have to be composite.) What is the largest possible value of this number?
2018 Team