Samantha’s square courtyard
(total area less than 100 m^2
) has an area equal to an integer number
of square meters. She decides to
install an octagonal fish pond in the
courtyard.
To mark the sides of the
pond, she draws lines from each
corner of the square to the midpoints
of the two sides not touching said
corner. She finds that the perimeter
of the pond, thus delimited, is an
integer number of meters.
What is
the area of the courtyard, and what
is the perimeter of the pond?
Determine whether or not N is a composite number, where
N = 675*2621 + 677*2610 - 1
NOTE:
A
prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself. A
composite number is a positive integer which has a positive divisor other than one or itself.
By definition, every integer greater than one is either a prime number or a composite number. The numbers 0 and 1 are considered to be neither prime nor composite.
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