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Archy [21]
2 years ago
9

Prove that 25^11 - 5^19 is divisible by 31.

Mathematics
1 answer:
Stells [14]2 years ago
7 0

Answer:

See below  

Step-by-step explanation:

                                        25¹¹ - 5¹⁹

Convert to base 5       = (5²)¹¹ - 5¹⁹

                                    =  5²²   - 5¹⁹

Factor out the GCF     =  5¹⁹(5³ - 1)

                                    =  5¹⁹(125 - 1)

                                    =  5¹⁹ × 124

                                    =  5¹⁹ × 4 × 31

31 is a factor of 25¹¹ - 5¹⁹, so the expression is divisible by 31.

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