6. In 1848 the mathematician Alphonse de Polignac conjectured that "Every odd number can be expressed as the sum of a power of 2

Question

6. In 1848 the mathematician Alphonse de Polignac conjectured that "Every odd number can be expressed as the sum of a power of 2 and a prime."
(a) Verify the conjecture for the numbers 61 and 119.
(b) Show that the number 509 demonstrates this conjecture is false.

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