# 2006 iTest Problems/Problem 18

## Problem

Every even number greater than 2 can be expressed as the sum of two prime numbers.

Name the mathematician for which this theorem was named, and then name the mathematician to whom he transmitted this theorem via letter in 1742. $\text{(A) Ptolemy; Archimedes}\qquad \text{(B) Goldbach; Newton}\qquad \text{(C) Lagrange; Goldbach}\qquad$ $\text{(D) Euclid; Plato}\qquad \text{(E) Goldbach; Bernoulli}\qquad \text{(F) Goldbach; Euler}\qquad$ $\text{(G) L'Hopital; Goldbach}\qquad \text{(H) Goldbach; L'Hopital}\qquad \text{(I) Ramanujan; Fermat}\qquad$ $\text{(J) Fermat; Ramanujan}\qquad \text{(K) Goldbach; Ramanujan}\qquad \text{(L) Goldbach; Fermat}\qquad$ $\text{(M) De Moivre; Cauchy}\qquad \text{(N) Cauchy; De Moivre}\qquad \text{(O) Goldbach; Cauchy}\qquad$ $\text{(P) Goldbach; Descartes}\qquad \text{(Q) Goldbach; Hilbert}\qquad \text{(R) none of the above}\qquad$

## Solution

The answer is $\boxed{\textbf{(F) } \text{Goldbach ; Euler}}$ since Goldbach's Conjecture is the theorem's name, and Goldbach wrote a letter of the theorem to Euler in 1742.