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7^a= 4^b + 5^c + 6^d diophantine

Source: 2009 Romania JBMO TST 2.1

June 1, 2020
Diophantine equationdiophantinenumber theory

Problem Statement

Find all non-negative integers a,b,c,da,b,c,d such that 7a=4b+5c+6d7^a= 4^b + 5^c + 6^d.
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