26:I[91452,["/_next/static/chunks/f915c07274536659.js?dpl=dpl_6MnXruQRBVToNztnTT8CLMLZMzdp","/_next/static/chunks/b100b36337f58b96.js?dpl=dpl_6MnXruQRBVToNztnTT8CLMLZMzdp","/_next/static/chunks/44f9947f31017eda.js?dpl=dpl_6MnXruQRBVToNztnTT8CLMLZMzdp","/_next/static/chunks/1f34752723866743.js?dpl=dpl_6MnXruQRBVToNztnTT8CLMLZMzdp","/_next/static/chunks/06238a0ba6e2450a.js?dpl=dpl_6MnXruQRBVToNztnTT8CLMLZMzdp","/_next/static/chunks/1fe50d1faa3d3f5b.js?dpl=dpl_6MnXruQRBVToNztnTT8CLMLZMzdp","/_next/static/chunks/a068ae4bba82be06.js?dpl=dpl_6MnXruQRBVToNztnTT8CLMLZMzdp","/_next/static/chunks/135849583f9affe4.js?dpl=dpl_6MnXruQRBVToNztnTT8CLMLZMzdp"],"ProblemHintSolution"] 21:["$","path","mthhwq",{"d":"m9 18 6-6-6-6"}] 22:["$","span",null,{"className":"text-foreground font-medium truncate max-w-[150px] sm:max-w-[200px] md:max-w-[250px] lg:max-w-[300px]","title":"Product of 10 factorials is 10-th power","children":"Product of 10 factorials is 10-th power"}] 25:T505,Given

10

positive integers with a sum equal to

1000

. The product of their factorials is a

10

-th power of an integer. Prove that all these numbers are equal.

Problem Statement