# July, 2019

## Ask Uncle Colin: Some Symmetric Algebra

Dear Uncle Colin, If I know that $a+b+c = 0$, how can I show that $(2a-b)^3 + (2b-c)^3 + (2c-a)^3 = 3(2a-b)(2b-c)(2c-a)$? - Something You Might Merrily Explain? Thanks! Regards! Yippee! Hi, SYMMETRY, and thanks for your message! As usual, there are myriad ways to attack this, of which I

## The Dictionary of Mathematical Eponymy: Sophie Germain primes

What are they? A Sophie Germain prime is a prime such that $2p+1$ is also prime - for example, 23 is a Sophie Germain prime since 47 is also prime. The largest known Sophie Germain prime has close to 400,000 digits; it is conjectured that there are infinitely many such