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Home » + \sec^2 \theta + \csc^2 \theta = 7 + \tan^2 \theta + \cot^2 \theta - Aurero

+ \sec^2 \theta + \csc^2 \theta = 7 + \tan^2 \theta + \cot^2 \theta - Aurero

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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We aim for the largest such $ N $, so start from 39 downward.
Check if 39 can be written as sum of distinct primes:
is odd â must include the only even prime, 2, or use odd primes only...
Try including 2: then we need sum of distinct odd primes â¡ 37 mod 2...
So check: 39 = 2 + 37? Yes, 2 and 37 are distinct primes.
Is 37 â¤ 39 and prime? Yes.
And 2 + 37 = 39, and distinct â valid.
Check if 39 is the maximum possible. Can we get 39? Yes.
Is 40 possible? No, upper bound is less than 40.
Is 39 the maximum? Yes, since 38, 37, etc., are smaller.

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