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Number of integral terms in (a^(1/2) + b^(1/q))^n

The same question, asked 2 times: 11 Apr 2023*, 30 Jan 2024. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    11 Apr 2023

    86
    The number of integral terms in the expansion of (312+514)680\left( 3^{\frac{1}{2}}+5^{\frac{1}{4}} \right)^{680} is equal to

  2. Question 2

    30 Jan 2024

    86
    Number of integral terms in the expansion of {7(12)+11(16)}824\left\{ 7^{\left( \frac{1}{2} \right)}+11^{\left( \frac{1}{6} \right)} \right\}^{824} is equal to