id: 05298105
dt: j
an: 2008d.00259
au: Hoare, Graham
ti: Sum = Product.
so: SYMmetryplus, No. 35, 6-7 (2008).
py: 2008
pu: Mathematical Association (MA), Leicester
la: EN
cc: F60
ut: number theory; proofs; arithmetic; integers; diophantine equations
ci:
li:
ab: Summary: Whilst scaling some Cumbrian mountains recently a property of the
number 6 was noted by a fellow walker, namely that $6 = 1 + 2 + 3 = 1
\times 2 \times 3$. I was challenged to prove that this is the only
triplet of positive integers whose product equals its sum. It reminded
me of the Pons Asinorum, as there cannot be many candidates. Here are
some thoughts as they kept me awake in the early hours of the next
morning.
rv: