public class IntroTasks {
    public static boolean is3Digit(int a) {
        return (a >= 100) && (a <= 999);
    }

    public static boolean isLast5(int a) {
        return (a % 10 == 5);
    }

    public static boolean isSameDigits(int a) {
        return (a % 10) == ((a / 10) % 10);
    }

    public static boolean isLeapYear(int a) {
        return (a % 400 == 0) || ((a % 4 == 0) && (a % 100 != 0));
    }

    public static String cat(int a) {
        //кот 1 21 31
        //кота 2 3 4 22 23 24 32 33 34
        //котов 5-20 25-30
        if (a % 10 == 1) {
            return "kot";
        }
        if ((a % 10 < 5) && (a % 10 > 1)) {
            return "kota";
        }
        return "kotov";
    }

    public static String getQuadraticEquationSolution(int a, int b, int c) {
        if (a == 0 && b == 0 && c == 0) {
            return "there are infinitely many solutions";
        }
        if (a == 0 && b == 0) {
            return "no solution";
        }
        if (a == 0) {
            return "one solution x = " + Double.toString(-c / (double)b);
        }
        double d = b * b - 4 * a * c;
        double sq = Math.sqrt(d);
        if (d < 0) {
            return "no solution";
        }
        if (d == 0) {
            return "one solution x = " + Double.toString(sq / a);
        }
        return "two solutions x1 = " + Double.toString(-sq / a) + ", x2 = " + Double.toString(sq / a);
    }

    public static boolean isPrimality(int a) {
        boolean flag = false;
        for (int x = 1; x * x <= a; x++) {
            flag |= (a % x == 0);
        }
        return !flag;
    }
}