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MATH / For how many ordered triples (x,y,z) of nonnegative integers less than 20 are there exactly two distinct elements in the set {i^(x),(1+i)^(y),z}, where i²=−1?

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problem

For how many ordered triples (x,y,z)(x,y,z) of nonnegative integers less than 2020 are there exactly two distinct elements in the set {ix,(1+i)y,z}\{i^x, (1+i)^y, z\}, where i2=−1i^2 = -1?
Plain-text mathematical notation (without MathML)
For how many ordered triples (x,y,z) of nonnegative integers less than 20 are there exactly two distinct elements in the set {i^(x),(1+i)^(y),z}, where i²=−1?
Original LaTeX notation
For how many ordered triples $(x,y,z)$ of nonnegative integers less than $20$ are there exactly two distinct elements in the set $\{i^x, (1+i)^y, z\}$, where $i^2 = -1$?

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
56b29e5a-cbf7-52ea-805c-2c569a6a9a7d
task_key
intermediate~5falgebra--test--56b29e5a-cbf7-52ea-805c-2c569a6a9a7d
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import