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Omni-MATH / Let a, b, c, d,m, n in mathbb{Z}^plus{} such that a^2plus{}b^2plus{}c^2plus{}d^2 equal{} 1989, aplus{}bplus{}cplus{}d equal{} m^2, and the largest of a,b,c,d is n². Determine, w…

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problem

Let $ a, b, c, d,m, n \in \mathbb{Z}^\plus{}$ such that \[ a^2\plus{}b^2\plus{}c^2\plus{}d^2 \equal{} 1989,\] \[ a\plus{}b\plus{}c\plus{}d \equal{} m^2,\] and the largest of a,b,c,d a, b, c, d is n2. n^2. Determine, with proof, the values of mm and n. n.
Plain-text mathematical notation (without MathML)
Let $ a, b, c, d,m, n \in \mathbb{Z}^\plus{}$ such that \[ a^2\plus{}b^2\plus{}c^2\plus{}d^2 \equal{} 1989,\]
\[ a\plus{}b\plus{}c\plus{}d \equal{} m^2,\] and the largest of a,b,c,d is n². Determine, with proof, the values  of m and n.
Original LaTeX notation
Let $ a, b, c, d,m, n \in \mathbb{Z}^\plus{}$ such that \[ a^2\plus{}b^2\plus{}c^2\plus{}d^2 \equal{} 1989,\]
\[ a\plus{}b\plus{}c\plus{}d \equal{} m^2,\] and the largest of $ a, b, c, d$ is $ n^2.$ Determine, with proof, the values  of $m$ and $ n.$

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Source and history

task_id
cb8f7349-94ce-5962-b447-f2883baa5de2
task_key
test--cb8f7349-94ce-5962-b447-f2883baa5de2
task_revision_id
1
config / split
/ test

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