阿迪爾汗
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
is my mother. She has baked a delicious strawberry pie.
are my grandparents. They are riding bikes.
is our house. I can see it from here.
are my parents. My Mom’s name is Ann and my father’s name is Tom
Простыми преобразованиями эту задачу не решить, будем использовать арифметику остатков.
1-ое свойство, которое понадобится
То есть мы спокойно можем заменить каждое слагаемое сравнимым с ним по модулю m. То есть каждое слагаемое в нашей сумме будем рассматривать отдельно.
2-ое свойство, которое нам понадобится:
То есть довольно аналогичная вещь в произведении
На нашем примере все увидим
Находим остатки по модулю 31
Рассматриваем первое слагаемое. Просто двойка не годится, нам нужно найти ближайшее к 31 число, превосходящее его (иногда там в отрицательные числа залезаем, например, 
, но сейчас это не нужно), нам повезло, это 32
Учитываем, что 
, получаем
То есть остаток от деления первого слагаемое на 31 получился равным 10. Прекрасно, аналогично со вторым
Остаток 21, чудесно. Выполняем последний шаг.
То есть остаток от деления исходного числа на 31 равен 0, следовательно, исходное число делится на 31, что и требовалось доказать.
