Counterexamples
One example breaks it
To prove "always" you need algebra.
To disprove it you need just one counterexample.
"n² + n + 41 is always prime" holds for n = 1 to 39, but n = 40 gives 1681 = 41 × 41. One value is enough.
Good places to look: 0, 1, negative numbers, fractions between 0 and 1, and 2 (the only even prime).
Always, sometimes or never
"Halving a number makes it smaller" is sometimes true: true for 6, false for 0 and for −4.
To say "never" or "always" you need a reason that covers every case.
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