In Mathematics
786 is a sphenic number. 50 can be partitioned into powers of two in 786 different ways (sequence A000123 in OEIS).
786 might be the largest n for which the value of the central binomial coefficient is not divisible by an odd prime squared. If there is a larger such number, it would have to be at least 157450 (see A059097).
In the New General Catalogue, NGC786 is a magnitude 13.5 spiral galaxy in the constellation Aries. Additionally, 786 Bredichina is an asteroid.
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“I must study politics and war that my sons may have liberty to study mathematics and philosophy.”
—John Adams (1735–1826)