Properties of a perfect sfourth

Number Theory Level pending

\[a_1^4=a_2^4+a_3^4- (a_4^2+a_5^2)\] is this true for all: \(a_1≥3\) where all variables are not necessarily distinct positive integers. note it is asking if a perfect fourth≥81 can be expressed as the sum of two perfect fourths plus or minus sum of two squares

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