24:["$","div",null,{"data-slot":"card","className":"bg-card text-card-foreground flex flex-col gap-6 rounded-xl border py-6 shadow-sm w-full","children":[["$","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":[["$","div",null,{"data-slot":"card-title","className":"text-2xl font-bold","children":"2008 appears on blackboard"}],["$","p",null,{"className":"text-sm text-muted-foreground","children":["Source: ","All Russian 2008, Grade 9, Problem 7"]}]]}],["$","div",null,{"className":"text-sm text-muted-foreground whitespace-nowrap","children":"June 13, 2008"}]]}],["$","div",null,{"className":"flex flex-wrap gap-2","children":[["$","span","12",{"data-slot":"badge","className":"inline-flex items-center justify-center rounded-full border px-2 py-0.5 text-xs font-medium w-fit whitespace-nowrap shrink-0 [&>svg]:size-3 gap-1 [&>svg]:pointer-events-none focus-visible:border-ring focus-visible:ring-ring/50 focus-visible:ring-[3px] aria-invalid:ring-destructive/20 dark:aria-invalid:ring-destructive/40 aria-invalid:border-destructive transition-[color,box-shadow] overflow-hidden border-transparent bg-secondary text-secondary-foreground [a&]:hover:bg-secondary/90","children":"number theory"}],["$","span","95",{"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":"greatest common divisor"}],["$","span","140",{"data-slot":"badge","className":"inline-flex items-center justify-center rounded-full border px-2 py-0.5 text-xs font-medium w-fit whitespace-nowrap shrink-0 [&>svg]:size-3 gap-1 [&>svg]:pointer-events-none focus-visible:border-ring focus-visible:ring-ring/50 focus-visible:ring-[3px] aria-invalid:ring-destructive/20 dark:aria-invalid:ring-destructive/40 aria-invalid:border-destructive transition-[color,box-shadow] overflow-hidden border-transparent bg-secondary text-secondary-foreground [a&]:hover:bg-secondary/90","children":"relatively prime"}],["$","span","21",{"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":"combinatorics"}]]}]]}],["$","div",null,{"data-slot":"card-content","className":"px-6 space-y-8","children":[["$","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":"A natural number is written on the blackboard. Whenever number

x

is written, one can write any of the numbers 2x \\plus{} 1 and \\frac {x}{x \\plus{} 2}. At some moment the number

2008

appears on the blackboard. Show that it was there from the very beginning."}}]}]}]]}],"$L26"]}]]}]