#1678 · Algebra · Inequalities

Minimum product of factorials

If $a, b, c, d,
ot $a r e$ p $p os i t i v e in t e g er s w h oses u mi se q u a l t o$ n $, s h o w t ha tt h e l e a s t v a l u eo f$ a! b! c! d!
ot $i s$ (q!)^{p-r}((q+1)!)^r $, w h er e$ q $i s t h e q u o t i e n t an d$ r $t h er e main d er w h e n$ n $i s d i v i d e d b y$ p$.

~20 minProof · checked by AIfactorialinequalitiesminimization

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIX. Inequalities, Examples XIX.b, No. 19

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