Do you know Brahmagupta?
Number Theory
Level
1
Let be a set of all numbers that can be expressed as the sum of squares of 2 integers (same or different), then which statement is true about this set?
is closed under division.
is closed under multiplication.
is closed under subtraction.
is closed under addition.
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1 solution
It's not closed under division because 1 , 2 ∈ S but 1 / 2 ∈ / S .
It's not closed under addition because 1 , 2 ∈ S but 3 ∈ / S .
It's not closed under subtraction because 1 , 2 ∈ S but − 1 ∈ / S .
It is closed under multiplication: ( a 2 + b 2 ) ( c 2 + d 2 ) = ( a c − b d ) 2 + ( a d + b c ) 2 . This is a special case of Brahmagupta's formula (see the wiki on Pell's equation for the general formula).