MHB Solving for $k$: $k^2=x+y$ and $k^3=x^2+y^2$

  • Thread starter Thread starter anemone
  • Start date Start date
Click For Summary
The discussion focuses on finding non-negative integers \( k \) that satisfy the equations \( k^2 = x + y \) and \( k^3 = x^2 + y^2 \). Participants explore various values of \( k \) and analyze the implications of the equations on the integers \( x \) and \( y \). The hint suggests considering the relationships between the sums and squares of \( x \) and \( y \). The conversation emphasizes the need for systematic testing of integer pairs to identify valid solutions. Ultimately, the goal is to determine all possible values of \( k \) that meet the criteria.
anemone
Gold Member
MHB
POTW Director
Messages
3,851
Reaction score
115
Find all non-negative integers $k$ such that there are integers $x$ and $y$ with the property

$k^2=x+y$ and $k^3=x^2+y^2$
 
Mathematics news on Phys.org
Hint:

Compare $2(x^2+y^2)$ and $(x+y)^2$.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
View full post »

Similar threads

Undergrad Finding the Largest (or smallest) Value of a Function - given some constant symmetric errors
  • · Replies 3 ·
Replies
3
Views
2K
Is This a New Expression for the Beta Function?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Partial Differential Equation solved using Products
  • · Replies 2 ·
Replies
2
Views
2K
MHB Finding $k$ for 2 Non-Negative Roots of $x^2-2x\lfloor x \rfloor +x-k=0$
  • · Replies 2 ·
Replies
2
Views
1K
MHB Prove Divisibility: $(x-y)^2+(y-z)^2+(z-x)^2=xyz$ yields $x^3+y^3+z^3$
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Is this Recursive Pattern in the Collatz Sequence Known?
  • · Replies 3 ·
Replies
3
Views
767
MHB What are the values of n and k in n+8=2^k when n!+8 = 2^k?
  • · Replies 8 ·
Replies
8
Views
2K
MHB Find the possible values of k: x+1/y=y+1/z=z+1/x=k
  • · Replies 2 ·
Replies
2
Views
2K
MHB 6.2.8 {{k,4},{3,k}}=k what is k
  • · Replies 3 ·
Replies
3
Views
1K
MHB Factorize 6(x^5+y^5+z^5)-5(x^2+y^2+z^2)(x^3+y^3+z^3)
  • · Replies 1 ·
Replies
1
Views
1K