23:["$","div",null,{"data-slot":"card","className":"bg-card text-card-foreground flex flex-col gap-6 rounded-xl border py-6 shadow-sm w-full","children":[["$","div",null,{"data-slot":"card-header","className":"@container/card-header grid auto-rows-min grid-rows-[auto_auto] items-start gap-2 px-6 has-data-[slot=card-action]:grid-cols-[1fr_auto] [.border-b]:pb-6 space-y-4","children":[["$","div",null,{"className":"flex justify-between items-start gap-4","children":[["$","div",null,{"className":"space-y-2","children":[["$","div",null,{"data-slot":"card-title","className":"text-2xl font-bold","children":"Polynomial Divisibility"}],["$","p",null,{"className":"text-sm text-muted-foreground","children":["Source: ","1977 USAMO Problem 1"]}]]}],["$","div",null,{"className":"text-sm text-muted-foreground whitespace-nowrap","children":"April 4, 2010"}]]}],["$","div",null,{"className":"flex flex-wrap gap-2","children":[["$","span","10",{"data-slot":"badge","className":"inline-flex items-center justify-center rounded-full border px-2 py-0.5 text-xs font-medium w-fit whitespace-nowrap shrink-0 [&>svg]:size-3 gap-1 [&>svg]:pointer-events-none focus-visible:border-ring focus-visible:ring-ring/50 focus-visible:ring-[3px] aria-invalid:ring-destructive/20 dark:aria-invalid:ring-destructive/40 aria-invalid:border-destructive transition-[color,box-shadow] overflow-hidden border-transparent bg-secondary text-secondary-foreground [a&]:hover:bg-secondary/90","children":"algebra"}],["$","span","39",{"data-slot":"badge","className":"inline-flex items-center justify-center rounded-full border px-2 py-0.5 text-xs font-medium w-fit whitespace-nowrap shrink-0 [&>svg]:size-3 gap-1 [&>svg]:pointer-events-none focus-visible:border-ring focus-visible:ring-ring/50 focus-visible:ring-[3px] aria-invalid:ring-destructive/20 dark:aria-invalid:ring-destructive/40 aria-invalid:border-destructive transition-[color,box-shadow] overflow-hidden border-transparent bg-secondary text-secondary-foreground [a&]:hover:bg-secondary/90","children":"polynomial"}],["$","span","35",{"data-slot":"badge","className":"inline-flex items-center justify-center rounded-full border px-2 py-0.5 text-xs font-medium w-fit whitespace-nowrap shrink-0 [&>svg]:size-3 gap-1 [&>svg]:pointer-events-none focus-visible:border-ring focus-visible:ring-ring/50 focus-visible:ring-[3px] aria-invalid:ring-destructive/20 dark:aria-invalid:ring-destructive/40 aria-invalid:border-destructive transition-[color,box-shadow] overflow-hidden border-transparent bg-secondary text-secondary-foreground [a&]:hover:bg-secondary/90","children":"modular arithmetic"}]]}]]}],["$","div",null,{"data-slot":"card-content","className":"px-6 space-y-8","children":[["$","section",null,{"className":"space-y-3","children":[["$","h2",null,{"className":"text-lg font-semibold","children":"Problem Statement"}],["$","div",null,{"className":"prose dark:prose-invert max-w-none bg-muted/30 p-4 rounded-lg","children":["$","div",null,{"className":"latex","children":["$","span",null,{"className":"__Latex__","dangerouslySetInnerHTML":{"__html":"Determine all pairs of positive integers

(m,n)

such that\r\n (1\\plus{}x^n\\plus{}x^{2n}\\plus{}\\cdots\\plus{}x^{mn}) is divisible by (1\\plus{}x\\plus{}x^2\\plus{}\\cdots\\plus{}x^{m})."}}]}]}]]}],"$L25"]}]]}]