Let b be a positive integer and let a be an integer with a four-digit base b expansion, with not all digits the same. Define Tb(a) = a′ − a″, where a′ is the integer with base b expansion obtained by writing the base b digits of a in ascending order.
A sequence aj, j = 1, 2, … is called a Sidon sequence, after the Hungarian mathematician Simon Sidon. if all the pairwise sums a¡ + aj where i ≤ j are different. Use Theorem 2.1 to show that the sequence a¡, j = 1, 2, … is a Sidon sequence when aj = 2j.
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