Question

Determina catul si restul impartirii numarului
7^32+4×7^30 la 53
(5^23+5^22+5^21) la 31
3^100+3^101+3^102+3^103 la 40
8^41+8^42+8^43+8^45+8^46 la 73

Answer 1

Răspuns:

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Explicație pas cu pas:

a) (7³²+4·7³⁰):53=(7²·7³⁰+4·7³⁰):53=7³⁰·(49+4):53=7³⁰·53:53=7³⁰.  catul, restul 0

b) (5²³+5²²+5²¹):31=(5²¹·5²+5²¹·5¹+5²¹·1):31=5²¹·(5²+5¹+1):31=5²¹·31:31=5²¹.  catul, restul 0

c) (3¹⁰⁰+3¹⁰¹+3¹⁰²+3¹⁰³):40=(3¹⁰⁰·1+3¹⁰⁰·3¹+3¹⁰⁰·3²+3¹⁰⁰·3³):40=3¹⁰⁰·(1+3+9+27):40=3¹⁰⁰·40:40=3¹⁰⁰. catul, restul 0

c) (8⁴¹+8⁴²+8⁴³+8⁴⁵+8⁴⁶):73=(8⁴¹·1+8⁴¹·8¹+8⁴¹·8²+8⁴¹·8⁴+8⁴¹·8⁵):73=8⁴¹·(1+8+64):73+8⁴⁵(1+8):73