A260819 Positive integer solutions [a',b',c',d'] of the equation 1/a + 1/b + 1/c + 1/d = 1, for a <= b <= c <= d, lexicographically sorted.

2, 3, 7, 42, 2, 3, 8, 24, 2, 3, 9, 18, 2, 3, 10, 15, 2, 3, 12, 12, 2, 4, 5, 20, 2, 4, 6, 12, 2, 4, 8, 8, 2, 5, 5, 10, 2, 6, 6, 6, 3, 3, 4, 12, 3, 3, 6, 6, 3, 4, 4, 6, 4, 4, 4, 4

Offset: 1

Author

Marco Ripà, Jul 31 2015

Keywords

• easy
• full
• fini
• nonn
• tabf

Comments

There are only 14 positive integer solutions for 1/a + 1/b + 1/c + 1/d = 1.

Examples

			The 2nd row is [2,3,8,24] and represents the solution 1/2 + 1/3 + 1/8 + 1/24 = 1.
List of all the solutions:
1/2 + 1/3 + 1/7  + 1/42 = 1
1/2 + 1/3 + 1/8  + 1/24 = 1
1/2 + 1/3 + 1/9  + 1/18 = 1
1/2 + 1/3 + 1/10 + 1/15 = 1
1/2 + 1/3 + 1/12 + 1/12 = 1
1/2 + 1/4 + 1/5  + 1/20 = 1
1/2 + 1/4 + 1/6  + 1/12 = 1
1/2 + 1/4 + 1/8  + 1/8  = 1
1/2 + 1/5 + 1/5  + 1/10 = 1
1/2 + 1/6 + 1/6  + 1/6  = 1
1/3 + 1/3 + 1/4  + 1/12 = 1
1/3 + 1/3 + 1/6  + 1/6  = 1
1/3 + 1/4 + 1/4  + 1/6  = 1
1/4 + 1/4 + 1/4  + 1/4  = 1
		

References

• W. Sierpiński, 250 problems in elementary number theory, Elsevier Science Ltd, pages 14 and 83-85.

Links

• Eric Weisstein's World of Mathematics, Egyptian Fraction
• Index entries for sequences related to Egyptian fractions

Crossrefs

Cf. A229941.