Math Is Fun Forum

simone

Member

Registered: 2007-10-05

Posts: 19

arithmetics

hi, could you please help me explaining the correct mathematical approach to this question? It's quite intuitive the reslt is 13, but I'm not able to reach it with a valid mathematical process.
thank you.

The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these integers?

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,243

Re: arithmetics

There are only 8 perfect squares of positive integers upto 75.
49+25+1=75, that is the squares of 7, 5, and 1 add up to 75.
Hence, the required solution is 7+5+1=13.
The only mathematical way I can think of a solution is let a²+b²+c²=75;
keep substituting values of 1 to 8 for a,b,c till you reach the sum 75.

simone, try solving this problem mathematically!
A number leaves a reaminder 9 when divided by 10, reamiander 8 when divided by 9, remainder 7 when divided by 8, remainder 6 when divided by 7, remainder 5 when divided by 6, remainder 4 when divided by 5, remainder 3 when divided by 4, remainder 2 when divided by 3 and remainder 1 when divided by 2. What is the smallest such number?

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.