perplexus.info :: Numbers : Triangular and Heptagonal Hindrance

Triangular and Heptagonal Hindrance (Posted on 2022-12-22)

Each of x and y is a positive integer that satisfies this equation:
x^oC=y^oF

Determine the minimum value of x+y such that:
x is a triangular number and, y is a heptagonal pyramidal number.
What is the next smallest value of x+y?

*** ^oF = (9/5)*^oC+32, where ^oF represents degree Fahrenheit and, ^oC represents degree Celsius.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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computer solution

| Comment 1 of 3

for n=1:1000

hept(n)=n*(n+1)*(5*n-2)/6;

end

x=0;

for x0=1:2000

x=x+x0;

y=9*x/5+32;

if y==round(y)

if ismember(y,hept)

disp([x y x+y x0 find(hept==y)])

end

finds

                                            ordinal
   x          y          x + y      triangular  heptagonal
 
  630        1166        1796          35          11
  820        1508        2328          40          12

1796 and 2328 are the sought numbers.

Posted by Charlie on 2022-12-22 10:28:40

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