Question

X=259 la puterea 3+n + 534 la puterea 5+n nu poate fi patrat perfect

Answer 1

x= 259 ^(n+3) + 534 ^(5+n)

x= 259^n * 259³ + 534⁵ *534^n= 1^n(259 *259³ + 534⁵ *534)= 259⁴ + 534⁶

259¹=(......9)
259²=(.......1)
259³=(........9)  =>259⁴=(......1)

534¹=(........4)
534²=(.........6)
534³=(.........4)   =>534⁶=(........6)

x=(.....1)+(......6)=(.......7)-nu este pp   numerele care se trmina in 2,3,7,8 nu pot fi patrate perfecte