100%
explainable
AXIOM
←
SENTINEL
←
OMEGA
Ω
Every answer has a proof.
ALGEBRA
▼
Solve
Factor
Expand
Simplify
Derivatives
Systems
Polynomials
Geometry
Trigonometry
Logarithms
Sequences
Inequalities
x² - 5x + 6 = 0
x² - 9 = 0
2x + 3 = 7
5x - 10 = 15
x³ - 8 (diff cubes)
x³ + 27 (sum cubes)
2x² + 5x + 3 (AC)
x⁴ - 1
6x² + 11x + 3
（x+2)(x+3)
(x+3)²
(a+b)(a-b)
3x + 2x - x
(x²-4)/(x-2)
d/dx (x⁶-4x⁴+3x²-1)
d/dx (x²+1)(x³-1)
d/dx (x⁷/7-x⁵/5+x³/3)
d²/dx² x⁴
x+y=5, x-y=1
2x+3y=12, x-y=1
Long division
Synthetic div
Remainder thm
Find all roots
Circle r=5
Rectangle 4×6
Sphere r=3
Pythagorean 3,4
sin(30°) = 1/2
cos(45°) = √2/2
sin²+cos² = 1
sin(2x) = 2sin·cos
cos(a+b) identity
tan(60°) = √3
log₁₀(100)
ln(e²)
log₂(8)
Arith a₁₀₀
Geom sum S₁₀
S∞ = a/(1-r)
Fib(20) = 6765
2x + 3 > 7
x² - 4 < 0
CALCULUS
▼
Derivatives
Integrals
Limits
Trig Calculus
Exponential
Chain Rule
Product Rule
Quotient Rule
Series
Taylor/Maclaurin
Definite ∫
d/dx (x⁵-3x⁴+2x³-x)
d/dx √(x³+2x)
d/dx arctan(x)
d/dx sec²(x)
d/dx xˣ
∫ xeˣ dx (parts)
∫ sin³(x) dx
∫ 1/(x²+1) dx
∫ x/√(1-x²) dx
∫ ln(x) dx
∫ eˣsin(x) dx
lim x→0 sin(x)/x = 1
lim x→0 (eˣ-1)/x
lim x→∞ (1+1/x)ˣ = e
lim x→0 (1-cos(x))/x²
lim x→0 tan(x)/x
d/dx sin(3x)cos(2x)
d/dx arcsin(x)
∫ tan(x) dx
∫ sec²(x) dx
d/dx cot(x)
d/dx e^(x²)
d/dx x²ln(x)
∫ xe^(-x²) dx
d/dx e^(sin(x))
∫ e²ˣcos(x) dx
d/dx sin(cos(x))
d/dx ln(sin(x))
d/dx (x³+2x)⁵
d/dx e^(tan(x))
d/dx √(sin(x²)+1)
d/dx x³eˣ
d/dx x²sin(x)cos(x)
d/dx (x+1)ln(x)
d/dx sin·cos·tan
d/dx (x²-1)/(x²+1)
d/dx sin(x)/cos(x)
d/dx eˣ/(1+eˣ)
d/dx ln(x)/x
∑ 1/n² = π²/6
∑ (-1)ⁿ/n! = 1/e
∑ 1/n! = e
∑ (1/2)ⁿ = 2
∑ (-1/3)ⁿ = 3/4
e^x = 1+x+x²/2!+...
sin = x-x³/3!+x⁵/5!-...
cos = 1-x²/2!+x⁴/4!-...
ln(1+x) series
1/(1-x) = ∑xⁿ
∫₀² x² dx
∫₀^π sin(x) dx
∫₁^∞ 1/x² dx
ERDŐS-STRAUS CONJECTURE
10M✓
▼
Egyptian Fractions
Decompose
Prime Tests
Mersenne
Fibonacci
Archimedes
Verify
4/127
4/1009
4/9973
4/9999991
4/8191
4/524287
7919 (1000th)
104729 (10000th)
M₁₃ = 8191
M₁₇ = 131071
M₁₉ = 524287
F₂₃ = 28657
F₂₉ = 514229
Prime ω=0 (50% SS)
Prime 1009 (Hard)
ω=3 (3·5·7)
ω=4 (3·5·7·11)
Shift 0 (n=3)
Shift 2 (n=17)
Mersenne M₁₉
Near 10M
Verify 4/5
Verify 4/7