MaplePrimes - answers and comments on Question, please help to solve this equation

isolve

Preben Alsholm — Fri, 16 Dec 2011 20:59:23 Z

Use isolve to get integer solutions. Then you will need to remove solutions which are not in NxN.

restart;
res:=isolve(61*a^2+1=b^2);
#The solutions as a list of lists [a,b]
RES:=map(subs,[res],[a,b]):
#The global _Z1 can take any integer value, so here are the integer solutions corresponding to _Z1 values from -3 to 3:
seq(normal(RES,expanded),_Z1=-3..3):
#However, these are not all pairs of positive integers, so:
ListTools:-FlattenOnce([%]);
select(type,%,[posint,posint]);

natural numbers

PatrickT — Fri, 16 Dec 2011 22:44:16 Z

@Markiyan Hirnyk

In my experience (French high school), N stands for the natural numbers while N* stands for N\{0}, that's N without the zero element. That would be my guess here.

so if my interpretation is correct, the last line of Preben's code would be select(type,%,[posint,integer]);

thanks

mad_man10 — Sat, 17 Dec 2011 01:06:14 Z

thank you very much

Agree

Markiyan Hirnyk — Fri, 16 Dec 2011 22:54:30 Z

@PatrickT Agree with you, but the asker typed N*⋅ N, not N*N. In my opinion every notion should be defined.

whole numbers

PatrickT — Fri, 16 Dec 2011 22:55:21 Z

Actually, if wikipedia may be trusted,

There is no universal agreement about whether to include zero in the setof natural numbers: some define the natural numbers to be the positive integers{1, 2, 3, ...}, while for others the term designates the non-negative integers {0, 1, 2, 3, ...}.

Some authors use the term "natural number" to exclude zero and "whole number" to include it; others use "whole number" in a way that excludes zero, or in a way that includes both zero and the negative integers.

further down the page, there is confirmation of the notation N*=N\{0}.

http://en.wikipedia.org/wiki/Natural_number

Nonstandard analysis

Markiyan Hirnyk — Fri, 16 Dec 2011 23:13:36 Z

@PatrickT The notion *N is used in nonstandard analysis. See http://en.wikipedia.org/wiki/Nonstandard_analysis