Let rad(n) be the product of the primes that occur in the prime-power factorization of n. For example, rad(360) = rad (23 · 32 · 5) = 2 · 3 · 5 = 60.
Show that rad (nm) ≤ rad (n) rad (m) for all positive integers m and n. For which positive integers m and n does equality hold?
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