[tex]n = |4 {}^{15} \times ( - 3) {}^{60} + ( - 4) {}^{45} \times 243 {}^{9} | \div 27 {}^{15} - ( - 2) {}^{90} + 2 {}^{16} [/tex]
[tex]n = |(2 {}^{2}) {}^{15} \times ( - 3 {}^{2} ) {}^{30} + ( - 4) {}^{45} \times (3 {}^{5}) {}^{9} | \div 27 {}^{15} - ( - 2) {}^{90} + 2 {}^{16} [/tex]
[tex] n = |(4 \times 9) {}^{30} + ( - 4 \times 3) {}^{45} | \div 27 {}^{15} - ( - 2) {}^{90} + 2 {}^{16} [/tex]
[tex]n = |36 {}^{30} + ( - 12 {}^{45}) | \div 27 {}^{15} - ( - 2) {}^{90} + 2 {}^{16} [/tex]
[tex]n = (36 {}^{30} - 12 {}^{45} ) \div 27 {}^{15} - 2 {}^{90} + 2 {}^{16} [/tex]
[tex]n = ( \frac{36 {}^{2} }{27} ) {}^{15} - ( \frac{12 {}^{3} }{27} ) {}^{15} - 2 {}^{90} + 2 {}^{16} [/tex]
[tex]n = 48 {}^{15} - 64 {}^{15} -( 2 {}^{6} ) {}^{15} + 2 {}^{16} [/tex]
[tex]n = 48 {}^{15} - 128 {}^{15} + 2 {}^{16} [/tex]
[tex]n = (2 {}^{4} \times 3) {}^{15} - (2 {}^{7} ) {}^{15} + 2 \times 2 {}^{15} [/tex]
[tex]n =( 2 {}^{4} ) {}^{15} \times 3 {}^{15} - (2 {}^{7} ) {}^{15} + 2 \times 2 {}^{15} [/tex]
[tex]n = 2 {}^{15} (2 {}^{4} \times 3 {}^{15} - 2 {}^{7} + 2)[/tex]
[tex]n = 2 {}^{15} (229.582.512 - 128 + 2[/tex]
[tex]n = 2 {}^{15} \times 229.582.386[/tex]
[tex]n = 2 {}^{15} \times 20.871.126 \times 11[/tex]
Rezulta ca N este divizibil cu 11.
