## Equation : x^2 + y^3 = z^4

$x^2 \; + \; y^3 \; = \; z^4$

$28^2 \; + \; 8^3 \; = \; 6^4$

$41328^2 \; + \; 288^3 \; = \; 204^4$

$48015100^2 \; + \; 9800^3 \; = \; 6930^4$

$55420360128^2 \; + \; 332928^3 \; = \; 235416^4$

$63955420452028^2 \; + \; 11309768^3 \; = \; 7997214^4$

$73804512448220400^2 \; + \; 384199200^3 \; = \; 271669860^4$

$85170343840128993628^2 \; + \; 13051463048^3 \; = \; 9228778026^4$

$98286503001614049040128^2 \; + \; 443365544448^3 \; = \; 313506783024^4$

$113422539294015341873095900^2 \; + \; 15061377048200^3 \; = \; 10650001844790^4$

$130889512058807571649797612528^2 \; + \; 511643454094368^3 \; = \; 361786555939836^4$

Determine the next values.

Establish the recurrence relation.

math grad - Interest: Number theory
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### One Response to Equation : x^2 + y^3 = z^4

1. paul says:

The next values are

151046383493325216709193157453628^2 + 17380816062160328^3 = 12290092900109634^4

The recurrences are for the square, cube and 4th power

{1189,-40426,40426,-1189,1}
{35,-35,1}
{35,-35,1}

Paul.