треугольные и квадратные числа
n = int(input())
L = [1]
k = 2
while L[-1] < n:
    L.append(L[-1] + k)
    k += 1

count_1 = 0
count_2 = len(L) - 1
ans = 0
while count_1 < count_2:
    if L[count_1] + L[count_2] == n:
        ans += 1
        #print(L[count_1], L[count_2])
        count_2 -= 1    
    elif L[count_1] + L[count_2] > n:
        count_2 -= 1
    else:
        count_1 += 1

print(ans)

очень легкая задача: поразрядное приближение
n, x, y = map(int, input().split())
ans = 0
n -= 1
step = 10 ** 9
while step > 0:
    while n > ans // x + ans // y:
        ans += step
    if step > 1:
        ans -= step
    step //= 10
print(ans + min(x, y))


Вырубка леса
a, k, b, m, x = map(int, input().split())
left = -1
right = 10 ** 20
while right - left > 1:
    middle = (left + right) // 2
    if x <= a * (middle - middle // k) + b * (middle - middle // m):
        right = middle
    else:
        left = middle
print(right)