Question

Aratati ca numarul natural n=[(5^3)^7:(1+2^2)10-5^10]:5^2 este patrat perfect
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Answer 1

[(5^3)^7 : (1+2^2)^10 - 5^10] : 5^2 = (5^21 : 5^10 - 5^10) : 5^2 = (5^11 - 5^10) : 5^2 = 5^10 × (5 - 1) : 5^2 = 5^10 × 4 : 5^2 = 5^8 × 4 = 5^8 × 2^2 = (5^4 × 2)^2