Egyptian Fractions - Complete Search
Generate all Egyptian fractions of length 2 and 3.
egyptian_complete(a, b, show = TRUE)
a, b |
integers, a != 1, a < b and a, b relatively prime. |
show |
logical; shall solutions found be printed? |
For a rational number 0 < a/b < 1, generates all Egyptian fractions
of length 2 and three, that is finds integers x1, x2, x3 such that
a/b = 1/x1 + 1/x2a/b = 1/x1 + 1/x2 + 1/x3.
All solutions found will be printed to the console if show=TRUE;
returns invisibly the number of solutions found.
egyptian_complete(6, 7) # 1/2 + 1/3 + 1/42
egyptian_complete(8, 11) # no solution with 2 or 3 fractions
# TODO
# 2/9 = 1/9 + 1/10 + 1/90 # is not recognized, as similar cases,
# because 1/n is not considered in m/n.Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.