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Strange recurrence

Source: Own. Malaysian SST 2023 P3

August 30, 2023
algebra

Problem Statement

A sequence of reals a1,a2,⋯a_1, a_2, \cdots satisfies for all m>1m>1, am+1am−1=am2−a12a_{m+1}a_{m-1}=a_m^2-a_1^2 Prove that for all m>n>1m>n>1, the sequence satisfies the equation am+nam−n=am2−an2a_{m+n}a_{m-n}=a_m^2-a_n^2
Proposed by Ivan Chan Kai Chin
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