Puzzle | Num3ers: 9, 12, 16 — Golden ratio

 

                                                                                             Part 1

 
 

9 12 16 A

 

                                                                                             Part 2

 

9 12 16 B

 

 

 
 
 
 
 
 
 
 
 
 

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Num3er 27918

 

27918

 
Solution:

27918 A

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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System of Equations: A^3 – B^3 = x^5 and A^5 – B^5 = y^3

 

SYSTEM EQUATIONS 1

 

Find another solution.
 
 
 
 
 
 
 
 
 
 
 

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Puzzle | two Heronian triangles (a,b,c) and (a,b,d)?

 

HERON 7

 
 
 
 
 
 

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Four consecutive num3ers having the same number of divisors

 
Here’s a list of all the sets of 4 consecutive numbers (< 10,000) having the same number of divisors.

Is it possible to find sets of 5 or 6 consecutive numbers having the same number of divisors?

Search for numbers larger than 10,000
 

DIVISORS 1

 
Paul found solutions for 5, 6, and 7 consecutive integers

DIVISORS 2

DIVISORS 3

DIVISORS 4

 
 
 
 
 
 
 
 
 
 
 

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Are there positive integers (x,y); 2/(1/x + 1/y) = √(x*y)

 

GM HM

 
 
 
 
 
 
 
 
 
 

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Pattern | 33…33^3 * 3

 

CUBES PATTERN

 
 
Solution:

CUBES PATTERN 2

 

then

CUBES PATTERN 3

 
 
 
 
 
 
 
 

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