A236391 Positive numbers n such that 100*n^2/(100+n^2) are integers.

5, 10, 20, 30, 70

Offset: 1

Author

Larry J Zimmermann, Jan 24 2014

Keywords

• nonn
• fini
• full

Comments

Rewrite 100n^2/(100+n^2) as an I : n=sqrt(100I/(100-I)), where a finite substitution for I results.

Instead of 100, we could use 72 and get n=8,24,48,64; we could use 162 and get n=54,108,144,150. Many other values are possible.

Examples

			for n=20, 100*20^2/(100+20^2)=I or 80.
		

Crossrefs

Cf. A162688.

Programs

Mathematica

Select[Range[1000], IntegerQ[100*#^2/(100 + #^2)] &] (* T. D. Noe, Jan 29 2014 *)